Production Systems and Supply Chain Operations Exercises

These exercises practise production systems and supply chain operations for demand, takt, capacity, bottlenecks, inventory, unit loads, supplier performance, yield, delivery, disruption planning, and validation. The purpose is not only to calculate a planning number. The purpose is to decide whether the production system can deliver real demand with controlled quality, flow, resilience, and evidence.

Assume deterministic inputs unless an exercise states otherwise. Real systems should also check product mix, setup time, staffing, learning curve, supplier variability, logistics constraints, quality escapes, maintenance downtime, data accuracy, and human workload.

How to Use These Exercises

For each calculation, define:

1. the system boundary and demand basis;
2. the unit of flow: unit, job, tote, pallet, order, batch, or shipment;
3. the constraint being tested: capacity, lead time, stockout, yield, supplier risk, or delivery;
4. the operating action triggered by the result;
5. the evidence needed to validate the planning assumption.

The common mistake is optimizing a local activity without checking the system constraint. A faster workstation, larger order quantity, or lower purchase price can make the whole system worse if it increases queues, defects, shortages, or recovery time.

For each result, state whether it supports staffing, bottleneck investment, WIP release, replenishment policy, supplier governance, quality improvement, delivery recovery, or disruption response. Supply-chain metrics should show which constraint changes and which evidence proves the change is stable.

Exercise 1: Takt Time and Required Staffing

A cell has available production time:

Customer demand is:

The manual work content is:

Estimate takt time and minimum number of operators before allowances.

Solution

Takt time:

Minimum operator count from work content:

Round up:

Engineering Comment

The result is a staffing screen, not a final line design. The engineer should also check balance loss, walking time, ergonomic load, changeover, quality checks, material presentation, training, and whether demand variation requires flexible staffing.

Exercise 2: Bottleneck Shift After Parallel Capacity

A three-step line has cycle times:

Step	Cycle time
A	45 s/unit
B	60 s/unit
C	50 s/unit

A second identical station is added in parallel at step B. Find the line capacity before and after the change.

Solution

Before the change, capacities are:

The bottleneck is B, so line capacity is:

With two parallel B stations:

The new bottleneck is C, so line capacity becomes:

Engineering Comment

The added station improves the line, but not to 120 units/h. The bottleneck moves. The next improvement decision should focus on C, unless quality, downtime, staffing, or material supply creates a different real constraint.

Exercise 3: WIP and Lead Time with Little’s Law

A warehouse kitting process ships:

Average work in process is:

Estimate average flow time. If the target flow time is 2.5 days, what WIP level is consistent with the same throughput?

Solution

Little’s Law:

Current flow time:

Target WIP:

Engineering Comment

The target requires about 220 fewer kits in process if throughput is unchanged. That may require smaller release batches, better material availability, fewer holds, faster inspection, or clearer priority rules. Arbitrarily cutting WIP without protecting flow can create shortages.

Exercise 4: Economic Order Quantity Screen

A purchased component has annual demand:

Ordering cost is:

Annual holding cost is:

Estimate economic order quantity.

Solution

EOQ is:

Engineering Comment

EOQ is a screening result. Real ordering policy should consider minimum order quantity, supplier lot constraints, shelf life, quality holds, transport unit loads, cash limits, shortage consequence, and demand variability.

Exercise 5: Reorder Point with Safety Stock

Average demand is:

Supplier lead time is:

Safety stock is:

Find reorder point.

Solution

Expected demand during lead time:

Reorder point:

Engineering Comment

The reorder point should be compared with actual supplier performance. If lead time variability, inspection delay, or demand spikes increase, the safety stock may be inadequate even when average lead time is correct.

Exercise 6: Unit Load and Replenishment Trips

A line consumes:

Each tote holds:

A tugger cart can carry:

One replenishment round trip takes:

Find totes per day, trips per day, and tugger time per day.

Solution

Totes per day:

Trips per day:

Tugger time:

Engineering Comment

Unit-load design affects labor, space, ergonomics, replenishment frequency, and line-side inventory. A larger tote may reduce trips but increase reach, weight, damage risk, or stock at point of use.

Exercise 7: Supplier Lead-Time Service Check

A supplier promises delivery in:

Actual recent lead times are:

Calculate average lead time and on-promise performance.

Solution

Average lead time:

On-promise deliveries are those at or below 15 days:

So:

Engineering Comment

The supplier is not performing to the promised lead time, even though some deliveries are close. Planning should use measured lead-time distribution, not only quoted lead time. The response may include supplier development, safety stock, alternate sourcing, or revised customer promises.

Exercise 8: Rolled Throughput Yield

A product passes through three process steps with first-pass yields:

Estimate rolled throughput yield. How many starts are needed, on average, to obtain 1000 good units without relying on rework?

Solution

Rolled throughput yield:

Required starts:

Engineering Comment

A final yield number can hide poor first-pass flow. Rework consumes capacity, extends lead time, and may create additional quality risk. Improving the lowest-yield step often has system-level value beyond scrap reduction.

Exercise 9: On-Time Delivery and Expedite Dependence

A plant shipped 100 customer orders last month. Of these, 92 shipped on time. However, 18 of the on-time orders required expedite transport that is not part of the standard operating plan. Calculate raw on-time delivery and stable on-time delivery without expedite dependence.

Solution

Raw on-time delivery:

Stable on-time orders:

Stable on-time delivery:

Engineering Comment

The raw metric hides instability. Expedites may protect customers in the short term, but they can increase cost, overload planners, create picking errors, and hide the real capacity or supplier problem.

Exercise 10: Supplier Outage and Stockout Timing

A part has demand:

An alternate supplier can provide:

Available safety stock is:

The primary supplier is expected to be unavailable for 4 weeks. Determine whether safety stock is enough and estimate maximum outage duration before stockout.

Solution

Weekly deficit during outage:

Stock consumed over 4 weeks:

Remaining stock:

Maximum outage duration before stockout:

Engineering Comment

The plan survives the expected 4-week outage with little margin. The recovery plan should check alternate supplier quality approval, transport capacity, allocation rules, demand priority, inspection delay, and whether demand could exceed the assumed 500 units/week.

Review Checklist

A strong production and supply chain solution should check:

• whether demand basis, product mix, time basis, and flow unit are explicit;
• whether local capacity changes are evaluated against the system bottleneck;
• whether WIP, lead time, release rules, inspection holds, and priority logic are consistent;
• whether inventory calculations include demand variability, lead-time variability, quality holds, lot constraints, and shortage consequence;
• whether unit-load choices consider ergonomics, damage, line-side space, replenishment labor, and material presentation;
• whether supplier promises are compared with measured lead-time distribution and quality approval status;
• whether on-time delivery is separated from expedite-dependent recovery;
• whether disruption plans include alternate-source quality, allocation rules, transport, inspection delay, and demand priority.

The result should lead to a decision about capacity, release control, replenishment, supplier governance, buffer policy, or recovery planning.